Bezier curve handles - precision modeling
Re. 1: To equalize the handle's lenght (without changing their angles) you may select the whole handle, press V-->Set Handle Type-->Free and enable the Snapping Tool (press the magnet icon and change its mode to Vertex). Rotate the shorter handle tip 180 degrees, then select the longer one and snap it to the shorter. Select the rotated one again and rotate it back to its place (input -180 while rotating).


Note: Sorry for an odd method to do it but nothing else comes to my mind right now:). The advantage of this method over Polosson's idea is you keep the angles of the handles, while when you change the handle type to Automatic you don't.

Re. 2: Change the Transform Orientation type to Normal and select the handle you want to move. Press G and input the desired axis (remember to press the button, which defines the axis twice to make a transformation along normal coordinates).


You may also just use scaling. Select desired handle tip and press S.